{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Derivatives Analytics with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Appendix &mdash; Python in a Nutshell**\n",
    "\n",
    "**Wiley Finance (2015)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/images/derivatives_analytics_front.jpg\" alt=\"Derivatives Analytics with Python\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dr. Yves J. Hilpisch\n",
    "\n",
    "The Python Quants GmbH\n",
    "\n",
    "<a href='mailto:dawp@tpq.io'>dawp@tpq.io</a> | <a href='http://tpq.io'>http://tpq.io</a>\n",
    "\n",
    "Python online training | <a href='http://training.tpq.io'>http://training.tpq.io</a>\n",
    "\n",
    "DX Analytics library | <a href='http://dx-analytics.com'>http://dx-analytics.com</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python Fundamentals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First Steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 + 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 / 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 / 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import sin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1411200080598672"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.7568024953079282"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.sin(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x ** 3 + x ** 2 - 2 + math.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.909297426825681"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34.141120008059865"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(a) = 34.141\n",
      "f(b) = 77.243\n"
     ]
    }
   ],
   "source": [
    "%run A_pyt/a_first_program.py "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.arange(0.0, 20.0, 1.0)  # (start, end, step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.,   1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.,\n",
       "        11.,  12.,  13.,  14.,  15.,  16.,  17.,  18.,  19.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a.resize((4, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.,   1.,   2.,   3.,   4.],\n",
       "       [  5.,   6.,   7.,   8.,   9.],\n",
       "       [ 10.,  11.,  12.,  13.,  14.],\n",
       "       [ 15.,  16.,  17.,  18.,  19.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  2.,  3.,  4.])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0]  # first row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 15.,  16.,  17.,  18.,  19.])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[3]  # fourth (=last) row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1, 4]  # second row, 5th (=last) element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 7.,  8.])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1, 2:4]  # second row, third & forth element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0. ,  0.5,  1. ,  1.5,  2. ],\n",
       "       [ 2.5,  3. ,  3.5,  4. ,  4.5],\n",
       "       [ 5. ,  5.5,  6. ,  6.5,  7. ],\n",
       "       [ 7.5,  8. ,  8.5,  9. ,  9.5]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   0.,    1.,    4.,    9.,   16.],\n",
       "       [  25.,   36.,   49.,   64.,   81.],\n",
       "       [ 100.,  121.,  144.,  169.,  196.],\n",
       "       [ 225.,  256.,  289.,  324.,  361.]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.,   2.,   4.,   6.,   8.],\n",
       "       [ 10.,  12.,  14.,  16.,  18.],\n",
       "       [ 20.,  22.,  24.,  26.,  28.],\n",
       "       [ 30.,  32.,  34.,  36.,  38.]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x ** 3 + x ** 2 - 2 + np.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -2.00000000e+00,   8.41470985e-01,   1.09092974e+01,\n",
       "          3.41411200e+01,   7.72431975e+01],\n",
       "       [  1.47041076e+02,   2.49720585e+02,   3.90656987e+02,\n",
       "          5.74989358e+02,   8.08412118e+02],\n",
       "       [  1.09745598e+03,   1.44900001e+03,   1.86946343e+03,\n",
       "          2.36442017e+03,   2.93899061e+03],\n",
       "       [  3.59865029e+03,   4.34971210e+03,   5.19903860e+03,\n",
       "          6.15324901e+03,   7.21814988e+03]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = np.arange(0.0, 100.0, 1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50.0 at index no. 50\n"
     ]
    }
   ],
   "source": [
    "for i in range(100):\n",
    "    if b[i] == 50.0:\n",
    "        print(\"50.0 at index no. %d\" % i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 divided by 17 gives 58.824\n"
     ]
    }
   ],
   "source": [
    "print(\"%d divided by %d gives %6.3f\" % (1000, 17, 1000./17))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = np.random.standard_normal((4, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.64371681, -1.25182043, -0.56391455,  0.3314386 ,  1.20390744],\n",
       "       [ 0.41091404,  1.67824248, -1.02596417, -0.02176213,  0.53048021],\n",
       "       [ 0.57600497, -1.55430075,  0.13509601, -0.6231574 ,  1.42761494],\n",
       "       [-2.45615932, -1.62936212,  1.66033378, -0.30442536, -0.55443482]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.6749854009795335"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.13374927004897669"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1148394461082733"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pylab import plt\n",
    "plt.style.use('seaborn')\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['font.family'] = 'serif'\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAFyCAYAAABSnWbdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmCRJUsUMYJIkSRX7f7pRWj0mqxRFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1129477b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(np.cumsum(b))\n",
    "plt.xlabel('x axis')\n",
    "plt.ylabel('y axis')\n",
    "plt.savefig('../images/A_pyt/line_plot.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlMAAAFkCAYAAAAE1r5gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDBBZtpcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112a3ce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = np.resize(b, 20)\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.subplot(211)\n",
    "plt.plot(c, 'ro') # red dots\n",
    "plt.grid()\n",
    "plt.subplot(212)\n",
    "plt.bar(range(len(c)), c)\n",
    "plt.savefig('../images/A_pyt/dots_bars.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## European Option Pricing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Black-Scholes-Merton"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of European call option is   15.655\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112a27898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run A_pyt/b_BSM_valuation.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binomial Option Pricing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of European call option is   15.654\n",
      "CPU times: user 2.42 s, sys: 10.8 ms, total: 2.43 s\n",
      "Wall time: 2.43 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "%run A_pyt/d_CRR1979_loop.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of European call option is   15.654\n",
      "CPU times: user 75.6 ms, sys: 11.5 ms, total: 87 ms\n",
      "Wall time: 86 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "%run A_pyt/e_CRR1979_vectorized.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of European call option is   15.654\n",
      "CPU times: user 2.24 ms, sys: 1.62 ms, total: 3.86 ms\n",
      "Wall time: 2.58 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "%run A_pyt/f_CRR1979_fft.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Monte Carlo Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of European call option is   15.603\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEFCAYAAAAfRLtkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1154f3ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run A_pyt/g_MCS.py\n",
    "plt.savefig('../images/A_pyt/histogram.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Financial Topics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD6CAYAAACxrrxPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1156b6be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run A_pyt/h_REG.py\n",
    "plt.savefig('../images/A_pyt/regression.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD3CAYAAAANMK+RAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1197dfe48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run A_pyt/i_SPLINE.py\n",
    "plt.savefig('../images/A_pyt/splines.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: -1.000000\n",
      "         Iterations: 18\n",
      "         Function evaluations: 36\n",
      "Global Minimum is -1.571593\n",
      "Local Minimum is  -1.570801\n"
     ]
    }
   ],
   "source": [
    "%run A_pyt/j_OPT.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of the integral is 1.718281828\n"
     ]
    }
   ],
   "source": [
    "%run A_pyt/k_INT.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Advanced Python Topics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Object Orientation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run A_pyt/l_CLASS.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "o1 = Option(105., 100., 1.0, 0.05, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.654719726823579"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "o1.value()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# o1.vega()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "o2 = OptionVega(105., 100., 1.0, 0.05, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.654719726823579"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "o2.value()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "73.345040765170197"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "o2.vega()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Input Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<_io.BufferedWriter name='A_pyt/option_container'>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "o1 = Option(105., 100., 1.0, 0.05, 0.25)\n",
    "\n",
    "o2 = OptionVega(105., 100., 1.0, 0.05, 0.25)\n",
    "\n",
    "import pickle\n",
    "\n",
    "options = open(r'A_pyt/option_container', 'wb')\n",
    "\n",
    "pickle.dump(o1, options)\n",
    "\n",
    "pickle.dump(o2, options)\n",
    "\n",
    "options.close()\n",
    "\n",
    "options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options = open('A_pyt/option_container', 'rb')\n",
    "option1 = pickle.load(options)\n",
    "option2 = pickle.load(options)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.654719726823579"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "option1.value()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "73.345040765170197"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "option2.vega()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options = open('A_pyt/option_container_2', 'wb')\n",
    "pickle.dump((option1, option2), options)\n",
    "options.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<__main__.Option at 0x1130f9128>, <__main__.OptionVega at 0x1130f9940>)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optionstore = open('A_pyt/option_container_2', 'rb')\n",
    "olist = pickle.load(optionstore)\n",
    "olist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(olist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<__main__.Option at 0x1130f9128>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "olist[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.654719726823579"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "olist[0].value()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "73.345040765170197"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "olist[1].vega()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Excel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "               Close   Returns\n",
      "Date                          \n",
      "2017-10-18  13043.03  0.003685\n",
      "2017-10-19  12990.10 -0.004066\n",
      "2017-10-20  12991.28  0.000091\n",
      "2017-10-23  13003.14  0.000913\n",
      "2017-10-24  13013.19  0.000773\n",
      "2017-10-25  12953.41 -0.004604\n",
      "2017-10-26  13133.28  0.013790\n",
      "2017-10-27  13217.54  0.006395\n",
      "2017-10-30  13229.57  0.000910\n",
      "2017-10-31       NaN       NaN\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmMAAAFdCAYAAABPUGo9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4W+XZBvBbsuS9HTu2s5zYycl09iCDEMreZZURZspo\nmR+jpVAKLYVC2ZQ9Shll71EghCQEMoDsfTLtJHa84m3LkjW+P6RzdI62bU3r/l0X1yUdHUnvIbb8\n6H2f93k0NpsNRERERBQZ2kgPgIiIiCieMRgjIiIiiiAGY0REREQRxGCMiIiIKIIYjBERERFFkC7S\nA+it+vq2uN0GmpOTiqamzkgPI+zi9bqB+L32eL1ugNcej9cer9cNxMe15+dnaLw9xpmxGKTTJUR6\nCBERr9cNxO+1x+t1A7z2eBSv1w3E97UDDMaIiIiIIorBGBEREVEEMRgjIiIiiiAGY0REREQRxGCM\niIiIKIIYjBERERFFEIMxIiIioghiMEZEREQUQQzGgmj79q24/vqrce21V+KVV17As88+hWeffQpt\nbW2q8zo62nH88fOwc+cO+diyZUtwwQVn49prr0RNTQ1EcSeuuupSvPTSc27v89JLL2Hu3Gl48cVn\nAx7bpk0bceWVF2P9+rW9v0AiIiIKOgZjQTR27HhMnjwV48eXY9Gia/D739+IyZOn4qabroXZbJbP\nW7z4a8ydOx+fffaRfGzBguNw771/x8GDlQAArVaDE088BVdd9Tu397nqqqsAAAsXXh7w2CZOnITS\n0pG9vDIiIiIKlZjtTenPe0v34JeddUF9zemjC3D+sWU9es5RR83Bq6++hLVrf8asWbMBAIcOHcCN\nN96ChQvPw/XX/x9SU1MBAKNHj8V5512Iv//9LygrG4WbbrrV7+u3trbi3nvvgs1mxbBhw7Fnzy6c\ncMLJOOOMXwMAnnjiYZjNZhQXD0JdnfP/x6ZNG/Dll5+hpGQ4DhyoxLXX3oB9+/bgsccewoQJk3D+\n+RfivvvuxsUXX45f/er4Hl0zEREROdlsvttpc2YsDAoLi1BbWwMA2LZtK8rLJyMnJxczZ87Gt99+\nrTp34cLLUVlZgby8AdBovPYUlWVmZmLhwsvQ2dmJm2++Dffd9xA++OAdAMCqVT/i4MGDuO22P+Gi\niy6FyWQEYP+huOeeO3HVVb/DRRddivLySXj99VcwZco03H//w9i8eQNWrfoBN9xwCwMxIiKiPrBY\nrXjgzXU+z+m3M2PnH1vW41msUKmpOYyBAwsBAEuXLkZycgr27NkFvV6PTz/9CGeeebZ87hdffIJL\nL7XnnM2ZMw8jRpQG9B5DhgwFAOTk5KCzsxMAsH//XgwZMkQ+p7h4EACgubkZra2t+Prr/wEA2tpa\noNXam7QOG1aCE088BcuXf4eLL76sj1dOREQU3+qaDNhb1erznH4bjEWLn39eA5PJhGnTZqC9vR3p\n6Rm44oqr5MfPP/9M7Ny5A6NHj0FFxX60tLTgsssWQaMB7rvvbrz44mvQ6/V+38fTLFpJyQisW+dM\n2K+urgIAZGdnIzs7G2eeeTYyMzPR0tKMrVu3AABaW1vQ1taGsrJRePvtN3HhhQv7+r+AiIgobpkt\nvpcoAQZjQbVz53Zs2rQB3d3d+M9/XobRaITZbMZTTz0Hq9WKRx75hyqwqqysQGZmFp599klMmTIN\nK1euwDnn/AYAMHRoCQ4frsZf/3oXrrrq9xg2rER+3quvvgoAePvtN3DJJVfgm2/+h717d2Pnzu3Y\nt28v2tvbsXz5d5g//1isWbMKDz54HwoKBgKw4Ztv/ofRo8fgr399AM899y8UFw9CbW0Nzj33NxDF\nnXj66cdxzjnnIyUlFXfeeRusVgtnyIiIiHrJbLH6PUfjL6ksWtXXt8XmwIMgPz8D9fVt/k/sZ+L1\nuoH4vfZ4vW6A1x6P1x6v1w3072v/cnUFPvx+Hz5/9EyvieBM4CciIiIKAavNhg+/3+f3PAZjRERE\nREFmtdnw24eWBXQugzEiIiKiILMEkCsmYTBGRERE1AMGoxkvfLYNh490eD2nrskAABhWmIHrz57g\n8/UYjBEREREFyGyx4v1le/DT9lo8+f5mr+dVNdgDtaPLizBlVL7P12RpCyIiIiI/2jpNeGPxLuyt\nakFTm72jTV2zwev57YZuAEBaiv9aoQzGiIiIiPx45qMt2HWoxe241WqDVutetaJDCsaS/QdjXKYk\nIiIi8sFms3kMxADnDJirji4zACAtxf+8F4MxIiIiIh+kZHxPvFXYb+fMGBEREVFwdJksXh976sPN\n2Fft3ghcWqZMDyBnjMEYERERkQ/dZvfZr2OnDAIAHKhtx99fX6t6zGA0Y9PeIwCA5MQEv6/PYIyI\niIjIB6NZPTM2akg2EnXeg6x/fegseaHReG1JKeNuSiIiIiIfTN32YOzkmUNx1rzh0OsS8NEK7z0n\ndx5oBgDcfdm0gF6fM2NEREREPixdXwUAGFOSA71jRkyv8xxCWazOJc1hhRkBvT6DMSIiIiIvrDYb\ntu1vBACMK8mVjze2dqnOMxjtpSw6HSUtpo7KhzaAJUqAwRgRERH50dBsQHO7MdLDiAhl8r4y/8tm\ns6nOa3PsnuxJfTEJgzEiIiLy6Q/Pr8YtT6+M9DAiQgrGXPtLmlx2WFqt9uCsJ/XFJAzGiIiIKCAd\nXZ6rzfdHZosVz3+6FevEOgBAokuOmGv9sKc/2oKmNqOzDVIA9cUkDMaIiIgoIKZuz9Xm+6PK2jb8\nvKMOr30tAgB0LsHYmXOH45RZw1CQkwIAqG7owK3PrERtYycAIDWZy5REREQUBMrcqG6z90r0/Y3F\nos4Jc50ZS0vW49xjSpGkV9cbe2fpHgBAahKDMSIiIuqjqvp2VSNsT5Xo+ytpV6TEW5HXqUK+x+M9\nCcZY9JWIiIjctBu6cfcrP6tyo7q9NMXuj0wus4Cuy5SS02eX4JMf9rsdT+HMGBEREfVFS4cJAOJy\nZqzbbMEXqypUx1yXKSXe2h31JBjze6YgCIUA/g5goiiK0x3HHgfQCaAdwEQAN4uiWON47HYAmQBy\nACwWRfEzx/FJAK4DsB9AAYDbRFE0C4KQDOARAFUARgJ4UBTFXQFfAREREQWdzWpzO9bQ0oWRgyMw\nmDD6fmOVnLSv5C0YA4A7L5mKB95YpzqWn50S8HsGMjM2F8CnAJShX4coineJovgPABsA3AUAgiDM\nBLBAFMW7AdwM4FFBELIEQdAAeBPA3aIoPgDAAuAyx2vdDOCA47UeB/BKwKMnIiKikLB4CMZe+nw7\ntlc0RmA04eMaiJUWZwIAkn3MdJUNynI75q1dkid+zxRF8QMAbS7H/uzyGu2O26cBWO04xwxgB4D5\nAEYASJFmzwCsBHCq4/apiudsATBREITMgK+AiIiIgs7bkuSOyqYwjyR8Nu894nasrtkAABg20Hef\nyaED03v9vn1K4BcEIRvACQDOcRwqgD0Ak7Q6jtVDHdBJx6XneHqs1dd75+SkQudlZ0M8yM8PrPlo\nfxOv1w3E77XH63UDvPZ4FE3XXdVk8Hg8OyslJOOMhmvfsXyv27HHbp6PHRWNmDah2Odzn7p1Ab5e\nXYHnP94CoGfX0+tgTBCELADPALhSFEVpzrIOgPLdMx3HvB339Ryfmpo6ezfwfiA/PwP19W3+T+xn\n4vW6gfi99ni9boDXHo/XHm3XXdfQ7vF4t9Ec9HFGy7UbDO4dBhKsVowfmh3Q+CaOyMWksgE4YfoQ\nt/N9BWe92k0pCMIA2AOxP4iiuF8QBGlm7EsARznO0QMYA2AFgH0ADI7NAAAwx3Gu63MmANgkiqLP\nWTEiIiIKLW/V9r/fVI0rH1yKmsb+Myly+EgHVmyqhsXqvOaTZw7FOfNH9Oh1kvQJuPHccoweltOj\n5wWym3I+gEsAFAmC8GcAjwJY7HjufwVBAOzLjB+KorhGEIRlgiA8APtuyltFUWx2vM5CAPcLglAJ\nIAHAa463eBLAI47XLgOwqEdXQEREREFX3+x5mVJq9/PZj/tx9RnjwjmkkLnrpZ8AqMtRnLegLGzv\n7zcYE0XxewDfuxye4uP8h70c3wgPgZYoigbYS14QERFRlJB2Tc4rL0KiLgHfrT+kerypzRiJYYWU\nwWivuu+rjEUosOgrERERuRnuKOkwe3yhavlOIh5slm/XNHbihidWoLIm8nlfwfD4DXPD+n4MxoiI\niMiNxlFeNEGrhbHbd4PwO19cg44uM/7++tpwDC2kxpXk9Kh6fjAwGCMiIiI3Vpu96KtGCyyYHFjZ\nfYvVFnOzY1+tqVTdHz8iL+xjYDBGREREbiwWezCm1WhQNjgLi04d4/VcXYKzSc9f//MLukzmkI8v\nGA7UtuF9l9piWWmJYR8HgzEiIiJy8+3agwCcbZEStO4NsW02G9oN3Uh0KcK+YmN16AcYBPe++ovb\nsUgEY+FdFCUiIqKY0tllL4SqdQnGtBoNXv5iB1Zvq/H0tJiVwZkxIiIiiiZ6x6yXVqMOxmyweQ3E\n0lP1IR9XX3krzcGZMSIiIoo4ZSmL0UOzAQAtHSbVOY78fo9SEqM/vLjjhdXy7RdvPwadXWY0txuR\nkcpgjIiIiCJsR2UTAHuemMYxI1aUlxrw860+AjXAHthpAGRGYBYKAEzdFnSb7QHnhceNhC5Bi8y0\nxIiNh8uUREREpPLKlzsAOJP3AWBsSW7Az7f5mjYD8H//+hE3/+vH3g0uCBpaugAAc8uLcPy0IREb\nh4TBGBEREal0dvWtNIXVRzBmNPkuIBsOUhHbtOToWCBkMEZEREQq0hKeq0WnjsExk4pxwzkTfD7f\nVzC2auvhPo0tGCoOtwIAWtpNfs4MDwZjREREpFI2KAsAcMXJo1XH50wowqUnjcawgRk+n2/zHMsB\nAIry0vo8vr56Y/EuAMCa7bURHokdgzEiIiJS0Wjs/80tL/L4eHJigsfjEl8zYxbFY54akIfTb44t\ni+j7SxiMERERkYrBaEFyYoK8k9JVUl+CMYvzMW/LoeFSXhr+PpSeMBgjIiIiFYPRjGQftcIStL7D\nB1+bKf+3ukK+bfVXAyNERhRnAoiOJVOAwRgREREpWKxWNLcbkZuZ1OvX8BVk7TrUonivyARjZovV\n71JrODEYIyIiIllzmwkWqw0DslJ6/RpdAZaviNTMmNligy4hekKg6BkJERERRVxrp73cQ0YP+0tO\nKhsgL/+9t2yPx3O+WFWhuh/JmbGEBM/5cJHAYIyIiIhkj7yzAYD/HZNHTyxW3dfrtMjN8L602dJu\nxEcr9qmORWpmzGKxQs+ZMSIiIoo2OyubYDDalxib2ow+z7385NF46Nqj5PtdJguG+qg/9sNm92Kv\n3ZbI7KbsttiQwGCMiIiIoo1yeXHCCP9lH/KzUzBqSDYAwGgy44Tp3vs8NnoI7l78bDveW7oHrR3h\nrYRvsVihi6JlyuhoykREREQRV1HTJt+eProgoOckaO1BjRVAoj4BZYOzsLeqxe285Ruq3I5V1rah\nsrYNJqsNC48b2btB90K3xcoEfiIiIoouuw42q+57K/jqSj7Nkf6VoNHAZlMXfvXXHPxIiyHgcfaG\n0WTBkZYu+b7FYuPMGBEREUWXNdtqevU8ZyxmD76kXYpWqw1ax+3mdt/5Z8HqinT3yz+h22zF2JIc\n/LKzDk/cOBcJWi1e/2YnVm+rxTVnjIMNNlistqhK4GcwRkRERGjt7O7V86TyFAmOKTKtY9nSYrVB\n59iQ6as9EgCMGprdq/dWMhjNqGroAADUbbTPtB1p6UJBTipWb7M3BH/hs23y+SlJ0RMCRU9YSERE\nRBHT2Nrl/yQPBmTbi8MOyk8H4AzKlGUrlPXEpo7Kx4W/UueHjS8d0Kv3Vlon1rsdu+OFNVgn1nk8\n31e7p3CLnpEQERFRxBgUeV1XnDI64OddcGwZivPSMH+Sve6YcmZMIgVmcyYUYtGpY1HX1Im3v9st\nPz4wN7VPYweAdC9Fap/5eKvH4wfq2jwejwTOjBERERHGl+QCAC49UcC88mI/ZzulJutx0syh8rKf\nVL9LOTMmrVKmJtkDJr1OXVB2iI/6ZIFKT+5Zx4CaI519fs9gYTBGREREsrJBWX16foKnmTFHNCY9\nlpWe2Kf38MTSw10AhUGYjQsWBmNEREQEsyOY6WvPRq1GCsacwZEUmGm06nOCKdDOSlIgWFLU99m4\nYGHOGBEREcFiUc9e9ZaytIVEuu0pCAukIXlnVzdqmwwYXpTp9Rzljs2ywVnYc8i98CwA/ObYMpi6\nrZg1dqDf9w0XzowRERGRPJOVoO1baOBpmdJm8x6M3XzeRL+v+bf/rMV9r631ueOz22wf/7nHlOLU\nWcO8npeeosfRE4uRqPfdCD2cGIwRERGRs15YX5cpPQRj8mt7mHULZCaurtleN6y53XsPy7pGe0J+\nfnaK22uOKHbOqEmbCKIJgzEiIiIK3jKl4/lvfCOis8sMwLmEqPHw2h1dZtQ2Brazcev+I2huN+LB\n/67HvupW+XhnVzfeWWpvcp6XmYzRw3Lkx3IykvDnS6fJ91OSomdGTMJgjIiIiGC2BGeZUrL7UAuu\nf2IFAGe7I09x3sNvb8Bv7/82oNf85If9eHvJbuw62Iy/v75WHvMbi3fJ5+h1WlUT8IeuPUr1GqlR\nVHlfwmCMiIiI0NRuhF6nDfrMUZfJLM+MaX3Mutn8tEyS1DU5m4pf/fByLFl7EIk6Zzjj2gBc59KD\nMpraIEmib0REREQUVjabDfXNBuRnp0DTx7ITGqif/8qXOzBrbCEAz7NuA3NTUdvYCbPF6lYMVjJo\nQBqqGjqQmap3C7beWrIbFyjaK0kNwJ+6aZ5qw8DN501EVUN7VCXuSxiMERERxbmOLjMMRguEISl9\nfi3XWG7TniMocPSv7DZb3M5P0tuDJ7PFBr2XqESaWSvISXULxgDgx82H5dvJjpmv9BR1on55aR7K\nS/MCu4gw4zIlERFRnOswdAPw3t+xJ7pM6oArI1WPr346AABod7yPkjSTZfFRtdXUbX/NPVUtHmfP\nDtW3y7dTk2NvnsnviAVBKATwdwATRVGc7jiWC+BBAPsAjARwpyiKtY7HbgeQCSAHwGJRFD9zHJ8E\n4DoA+wEUALhNFEWzIAjJAB4BUOV4rQdFUdwFIiIiCplv1x7EzsomXHf2BJgdgZBrflVvbNxdr7pv\nVARnZ8wZLt++5/Lp2F/Tih0VTdhb3QqLxXM7o9qmThxpNcr3m9q81xq7+7JpIanuH2qB/F+fC+BT\nQLUI/ACAJaIoPgjgE9iDKQiCMBPAAlEU7wZwM4BHBUHIEgRBA+BNAHeLovgAAAuAyxyvdTOAA6Io\n/gPA4wBe6ftlERER9X9b9x/Bwbp2bNrTgEN17f6foPD2kt3YsLsBja1dciDU17IWgLNRuMTY7QzG\nlMnzwwozcMykQXJdM08zY5/9uB9/emGN6tih+g6v7+2rQn808xuMiaL4AYA2l8OnAljtuL3ScR8A\nTpOOi6JoBrADwHwAIwCkiKJY4+E5pyqeswXAREEQYvP/JhERUZh0mcx47N1NuOffP+PJDzbjL//+\nOeDnKlsHNTR3+SzK2lOuOV2+lh+V79nSoS7o+skP+/DJj/v7PJ5Y0NuF1QI4A7RWADmCIOgcx3co\nzmt1HKuHOqCTjru+lvKxVviQk5MKnZddF/EgPz96GpyGU7xeNxC/1x6v1w3w2uNRT677pU+39Pr5\ny9cdlG+npCUhybHDMDU1sc//70cOzUF982GPj3l6bWmm677X1uLzR8+Uj3+2sqLH7x2rPze9Dcbq\nAGQAaIY9P6zJkf8lHZdkOs71dhx+HvOqqSmwar39UX5+BurrXScr+794vW4gfq89Xq8b4LXH47X3\n5LprGzvx2Yp97sdrW33W8pLsqmiUb//1Zecy4Cff78UZR3nv6xgIjY96YZ6ur7nd6PPxQN1w9oSo\n/rnxFSj2NlPvSwBSSds5jvuq44Ig6AGMAbAC9kR/g2MzgK/nTACwSRRFn7NiRERE8ay+xeDx+K6D\nzQE93xpggdXekOqUuZaWGJCV7PF85dLof7+179+Tmn73xOCC9B4/J1r4DcYEQZgP4BIARYIg/FkQ\nhBQAdwI4XhCEPwM4G8BtACCK4hoAywRBeADAUwBuFUWxWRRFG4CFAO4XBOEvABIAvOZ4iycBDHO8\n1q0AFgX1ComIiPqZtk57iYjjpg5WHf/n2xsCer7BaA76mCTSbsYErQYFOc66Zf93/kSP5yuDse/W\nHQIA7Khs6vH7JiXGbuqS32VKURS/B/C9y2EDgKu8nP+wl+Mb4SHQEkXRAHvJCyIiIgqAFIyNGpKN\ndbvq0dTmXOrbW9WC0kFZAIC6ZgOefH8Trjx1DEqLs+RzDEb34qsAkJmW2OexScukNptNVc0/yUvl\n+zPnDsfLXzjTza02G554f5PbeaXFmdhb7X3hLCWGgzEWfSUiIooCbZ0m3PPvn1HrJye6tcOEd77b\nDcBeUPWGcyaoHv/Hm+sBABU1rbjj+dU4fKQTD7vMmHmr1XX5yaN7O3yZFH9ZberG4MlegqXpowtU\n972V6FgwZRCeumkeygZl4ZRZ7nltwaiRFimxO3IiIqJ+5Jp/fIeDde340wtrYLXZ8NwnW/GxI0m/\nvtmAPYdaAAAffr9Xfk5GaiJKCjMxqWyAfEzKB/tgufM8U7c6B6u6wXOtrtyMpD5fhxbOmTFlVQtv\nPSFdNxwoE/qVEnUJSE/R485LproFcAD63FMzkhiMERERRYHykc6A6qPv9+GXnXX4fFUFzBYr/vj8\najzw5jqYui3o7HLme2U42hd1e6hen5bsvbWRyWz1OJPkmnTfGxrHy1ptNtQ2Omf5vM1cuVbM95a8\nr8wJS0mK3SVJTxiMERERRYHC3FT59v/WVMq3lbNaTe1G7K5qke+nOYKnYycPcns9X8t2VqsNep37\nTFJaEIKx4gFpAICyQdkBne86o+UpsATUuzGTk2Kv/6Qv/etqiIiIYozZYsVTH2xGlZelw+2KmmDK\n1kB5mUnyrNKkkQNQXpqHzXuPAAAOH+nA6m018MZitTlmmtSJ/N6S7HtiXnkRkvUJKC/Nw/VP/NDj\n5x+s9ZwzptyZqY/h/DBP+tfVEBERxRir1YYdlU2qHZFKz36y1ePxh66dLd/WaDS4/mxnIv9bjnpd\nXt/TZgtK4OVJglaLWeMKkepjmdSXr3464PV1JbGcrO9J/7oaIiKiGGOx2lCUl+r/RBeuie+6BC2m\nCvkA1H0eyxxlLmyOxH6bzQabDUhOjN3FMdf+l7Eudv8liIiI+oHlG6vk/ox9JRVQVRZ13ePIMVsr\n1mP66AJ0mexLk+kp0R8CnDVvOI6eWAyTS1K/RqPB+QvK8N6yPREaWXBxZoyIiCgCOrvMWCfWo6oX\ngdhZc4d7PC4FYwmOZbwTpg+RH3tvqb02WZvBXjA2T5EQf+yUQUGpMeaNtOuzJ06eNRRnzBmO7PQk\nFGSnuD2+YIr7poVYFf1hMRERUT/08Q/75PY/PXWG12DMHoTVNdl7V54wfQgsFhu+W38Ic8uLYeq2\n4E/PrwagTtZfeILQq3H4c/N55fh4xX7ceckUn+flZSXjSIu6EK2/JH29rv/MJ/WfKyEiIoohv+ys\nU93/wyXTAnrebRdM8vpYgksuVXKiDqOH2UtMpCbp8NGKfZDqsIYqgV+pvHQA7rliOvQ63+913zWz\nUTY4y+c5rpT1yWaMcS8CG0sYjBEREUVAqyLJPlGnxbxJ6qXCaR6qzAPA0IEZXl/TNak/JSlBXrI0\nW61Y/MtB+bEkfQIKslM8LgGG25CBGbjsJPUyaU8q6l9zxrhgDymsuExJREQUZtLORom05DZzzED8\n56udALy3JvK1fJegCMbGDMuBRqORzze7JMHnZCbhgWtm9XzwIZLosuzYk/2SsdwKCWAwRkREFHau\nuWJSMJaodwYk8yYWq2ayJDoPlfPlxxS1uKqP2DcGSGUgVmyqVp07OD/drRVRJLkGY4FEY789bUzM\nB2IAgzEiIqKwe2vJbtX95nb7kqUysEjUaZGkT4CxW10lX1n81FVrp3Pps8XxmlLx1SOt6qKyg/PT\nezHy0HFNyA8kxJo9vig0gwkz5owRERGF2cAc/3laiTqtHIhlpOpx3NTBGDXEd7/H7HT3pc3B+fZe\nkcpZsN+fNT7qdiO6JvlPHpkfoZGEH2fGiIiIwqiqoQO1jtITnqQm6dBpNDt6R9qdPrsEx00b4vU5\nkhNmDFE1GQfss21DC9JR12xAbmYy6poMXjcHRJKyqv6ksgEYXBBdM3ehxGCMiIgojF76fJvPx/9x\nzSy0dXar2hWlJAX25zpVcd75C8rk23qdFl0mC6obOlTnRBPlEu3s8YURHEn4Ree/CBERUT9U32zA\ngdp2AEBpcSb0Oi12HmhWLT9mpCYiIzVR9bysNPV9b5QNtE+aOVS+Xel4TwDoVLRKila6KFtCDTUG\nY0RERGHy2tc75du3XjAJtY0GPPXhZpx99AiP5995yVSsF+sxdnhuwO8xr7wImS7Bm9li9XJ2dLJY\nbP5P6kcYjBEREYXJ9oomAMBN55YjOVGHYYUZePS6OV7PLxuUhbJBPatMf8UpY9yOzRo7EGu21/Zs\nsBGUlBhfM2PxdbVERERRYGxJTljfLzU5tuZe+kPtsJ5gMEZERBQGh+qdeVv+ejUGm7JNUiy0Doqv\nUIzBGBERUVh8vGJfxN57854j8u14KhkRKxiMERERhcH4EXkAgJNmDPVzZvANGegMwNzaDkUhzowR\nERFR0FisVnR2dWPNthoAQNngniXkB8Pps0vC/p69MWOMvRhtcZS1agq12MroIyIiijFvfbsbyzZU\nyfdHFGeGfQxJemeOWk6Ge8ukaHHNGeNw2UmjAy5y219wZoyIiCiElIEY4Ll/ZKgpE/iVhWGjjUaj\nibtADGAwRkRE1O/FWaWImMNgjIiIqBfaDd3o7Or2eY7NFh2V5MNdSoN6Jv7mAomIiILgxid/AAD8\n+45jvZ4j9YGcWJqHTXuPeD0v1LLSEnHNGeNQUpgRsTGQdwzGiIiI+mBnZRNGD/NcUX9/dat8+9Sj\nhkW0rMSGvyFvAAAgAElEQVTMsQMj9t7kG4MxIiKiHmrtMMm3P19VoQrGmtuN+HD5XqzcWiMfG1Gc\nidPnDA/rGCl2MBgjIiLqoeqGDvn2jsom+XZTmxG3PrPS7fysCOygpNjBBH4iIqIeOlDX7vG4p0AM\nAPRRXE6CIo8/HURERD1Uc6RDdb+ypg1mi9Xr+foYaEFEkcOfDiIioh5avrFadf+VL7ejy2Txej6D\nMfKFPx1EREQ9YOq2B12Jeuef0EP1Hdiwu97rc0YNyQ75uCh2MRgjIiLqgY4ue+2wySPzVcdf/d9O\n+fZzt85XPRaPLX4ocAzGiIiIeqCxrQsAkJqsDrAGZCUDAG6/YJKqMTeRPwzGiCjorFYbvl17ELsO\nNuPWZ1bi658O9Oj5ja1dUdNGhsjV8vX2xt8mlxyxDkdrpKIBaQDsVfcBZ5BG5E2f5k0FQbgdQAmA\nBgAjASwCkALgQQD7HMfuFEWxVnF+JoAcAItFUfzMcXwSgOsA7AdQAOA2URTNPRlLTWMnHnt3Ixad\nOgbCUM+VkIkoPJauP4S3l+yW77+3bA9OmjnU7TxTtwX7D7eqfme37W/Eo+9uBAAsmDoYlxw/KvQD\nJvJhxaZqNLZ24ax5IwAAeses17gRuRiUn473lu0BABiM9uAs1bEkeelJo/H8p1txyYlCBEZNsaTX\nwZggCIUA/gRggCiKVkEQPgVwNoB5AJaIovieIAinA3gEwCWCIMwEsEAUxVMEQdAB2CEIwvcAWgG8\nCeA4URRrBEF4FMBlAF7pyXi+XFWBhpYuvPzFdjz8+zm9vSwi6iOrzYbPVlYEdO6fX/4JDS32JZ9J\nZQNw47nleOL9TfLjNUc6QzFEoh75z1f2XLA5E4qQn50CnVYDACjOS8OssYVISNDIXz40GufOyZyM\nJPxp4dTIDJpiSl+WKTsBmGCf6QKAdADbAJwKYLXj2ErHfQA4TTrumPXaAWA+gBEAUkRRrPHwnIBZ\nHSsaR1qNPX0qEQXRY+9uRLuh2+95bZ0mORADgI17GgAAFqtzeXL+lMHBHyBRDxxSFHe999VfAABm\nx89ogqOQa4IjOAMAmw3QaDQg6olez4yJotjqWHZ8VxCEwwAOAdgD+zJjm+O0VgA5jpmwAtgDMCge\nKwBQrzhfedynnJxU6HTOBMk91S3y7SsfXIqPHjq9X9d1yc/PiPQQIiJerxuInWvfXtHk8bgJGgzK\nT5fvb1nrnkfmeo3Pf7QZY289BsOLs4I7yBgRK//moRAt1752d4N822A0Y9P+RnmZctjgbORkJCM7\nK0X1nL6MPVquOxLi+dr7skw5CcDtAKaIomh2LC/+BUAdgAwAzbDPmjU5HpeOSzId53o77lNTk3r5\nojAnFfVNBvn++9/uxPHThvTiyqJffn4G6uvb/J/Yz8TrdQP949rfW7wTC09w5s5UVLW4nVNX1+p2\nbOuuOqTr++8XK2/6w795b0XTtVfXqsfx1cr98kqMuasb9V3d6OhQr8j0duzRdN3hFg/X7ivY7Msn\n3CAAjYpE+8MAkgF8CeAox7E5jvtQHhcEQQ9gDIAVsCf6Gxw5aK7PCZjVZedVRoq+py9BRCE0wGX2\n4LBLOxkA2Hmg2e3YD5sPh2xMRJ7c+++fceWDS2G2WGEyq1sc7TrUgj1VLcjLdDb+1mnj78sCBVdf\ndlN+DeAUx4xYM4DxAG4GYATwkCAIowCUArgNAERRXCMIwjJBEB6AfTflraIoNgOAIAgLAdwvCEIl\ngAQAr/V0MN0uvzBaLdfsicLNYnXvzTdnfCFWbq1R1WSyWm1Ys63W7dyH397gdmxHpedlT6Jgs9ls\n0Gg0chPwB/+7HqVelsiV+cn8e0N91ZecMQvs5Sg8ucrLcx72cnwj7GUxeq3bbHG5771hKxGFRnun\ne+J+6eAsrNxao/qd3HHAGWANGpCGqgb3WbI5EwqxckuN23GiUFn00DLV/X3VrdhX7b50DgCFuany\nbV2CMxibPtpvyjORm5ifWzWaLFi55TD2H1avNZstDMaIwm3z3iOq+0/eOBdZqYkAnL+TW/cfwac/\n7gcApCQl4I6FU/DXK2eonvfb08Zg0alj5fuNrV0giqSbzytX3T9q3ED5droiLeZ3Z40P25io/4j5\nYOyZj7fglS93uB03W1i9myjcKlySnTNSE+VdzdLM2GPvbsKeQ/bk/YuPH4W0ZD2GFKRj/qRi+Xl6\nnbqVzO5D7sn+RMG0o6IRSYneWxgNKVAnXyt/RtOZo0x9FPPB2Nb9jR6Pc2aMKPwaW9xnsHSOWkye\nfieV/fuUt/WO5yw8aTQAz7loRMHS1mnCw+9shNGlvZFSVnqi6r5yabJoQBqOnliM33NWjHqp37aR\nZzBGFF4WqxX7Drvn1+gcM2OfraxAcqL6I0c5E1HT6CxXI82mFTjycpgDSqH0z7ecG0cu+NVITB9d\ngFufWak6R6vRICNVjzZHXqSyjqVWo8HlJ48Oz2CpX4r5mTFvjN0W1DV14uMV+xiYEYVBS7tJ/kMF\nACdMt9f5k2a5AMg9/CTK2TBTt3NWQmoSnuh43LW8AFEwKTeQlJfmIScjSfX48CJ7o5nHb5grH+vP\nRcUp/GJ+ZqwwN1X1jVryxapKHKhtx+a9R9BlsuDC40ZGYHRE8cFgNOOBN9cBAOZOKMIJM4agOC8N\ngHNmzBNlMJaR6lwG6nIsF0mPmxmMRZ1D9e14+sMtOHbKIJwww70JfKxoanOWqPj3HcfKt/940WQc\nqG2HXq/F/In2fEatos2Ra14jUV/EfGjva9ZL2tn17dqDbo+t3HIYby3ZFbJxEcWTTXsb0Oiou/Tj\nlsMYnJ8u117yNYOgXKb81VRnH8rJowaonstlyujz0ff7UNdswDtL96hqwdU1deL7jVURHJl3rsXB\nAaCyxnPVd2FoDo6fPgTHTBrksdekMmeMqK9iOhizWm2qRsO+fLv2IL5cXSHff+XLHViy9pAczH34\n/V689Pn2EIySqP/r7DLLt+dOKFI9luQjGMtVLAeNGpKNp26ah5f/sAAJjormSVymjLiWdiOWrD0o\nLx1LukzOf/N9it7Ad7ywBq99LWKPh3ZXkfTS59vx24eW4fCRDrzyxXa5mb20OeTcY0oDep2BOfZO\nEgXZKX7OJApcTC9TtnaaAj737SW7AQBHTyxGsuLbeLfZCl2CFl+urgRgr2/k6VsQEXn31Rpn0+/L\nThZUj2WlJ2F4UYZbLcD0FL3bUo9riQBpZsxk9r7LjULr/562J7JnpiVixhhnbS1jtzNAlpb6Wjuc\nn8nRNJu5/3ArVm+zFxC+66WfAACdRjMuPn4UNu6xNwIfOTiwZvQ3nTcRDS0GVdN7or6K6ZkxpTPm\nlOC+387EwhNG+TzvqzUH0KL4wOjsMqO53ZkzUOFlypqIPNuwqx5HHEVZbzy3XJ7VUrr7sulux4YV\nem+aK0lkzlhESbNHANBhUHdXsChSRJaur3I7f+n6Q9hW4bn0ULh5mqXbsLsBtz27CofqOpCo06Js\nUGDBWGFuKsYPzwv2ECnOxfTMmDJf7Kx5IwDYW6u8udh7LtjXPx/AVCFfvn/7c6tUj1fUtMk7Z4jI\nv399tEW+PalsgN/zRw7OwvxJxZgwwv8fNGmZUjkLQ+FTVd8u325UJLoD9hlP1Ckeb+2CUbEjdp1Y\nj3VivSopPlKklRFPKmvbkKRP4IoIRVTMzoy1dZq8Fny98pQxPp/bbnDvnyeR8gGIKLjys5MB2Hek\nzR5fpNo96Y1e771gLIVe9RHnTvUvV1fKeWN1TZ3Ysu8Ifj1vuPz4bc+uwn2vrQ37GAMh/ex5owwi\niSIhZoOxe1/9Ba9/LQIAhg5Ur91PLPP9jbuu2eD1sZb2wPPQiOKdMqm7dJDvGeWLj7enEJw8a1jA\nry9V77dY/bc3O1DbhiUedk5T7x12aeBeUdMGo8mClx0t6GJlxjInw3cwdtrskvAMhMiLmF2mVNaG\nGTUkW/WYv2J8vqasDymm5YnIty5F+5g7Lp7i89zy0gF4+Q8L5JIXgUhwnGsJYGbs3ld/AQCMH5GH\nQkflfuobKeld8tpXO3FAsTSpS9Bg0IA0VdHUaLTrYLPPx0cFmLxPFCoxOzOmpEtQX4Zry5WeUCWs\ndnVj9dYadHMnF5FHG3fbd6Il6rUeE/dd9SQQAxR9LQOYGZNYe3AueWaz2fDKl9vRoShZAkAViAH2\nul3KDVGeBGuJ+YXPtuH+N9b26vUSHcvd91w+XbW0Kkljo2+KsH4RjCV4+IC/c+FUzBhTENDzy0vz\n8MSN9jYXynpJ//pgM176YjvW72oIzkCJ+hkp1+bXjg00wZYgLVP24A/wul31IRlLPNm2vxErt9S4\nHU9LVn/RNZqsPnNwAfXsaV/8tL0We6ta0eyykcAXm82GippWWCw2lBZnYlhhBk6fMxx/vXKGqpek\n63URhVu/CMY85ZOUDc7CtWeOx9lHO/9I5GYmuZ0H2L99pybZfxk7upwfLLsO2bdD96SeGVE8Wb6x\nCkn6BLkPZbAlaDXQaPznjD3x/ib59scr9qnqXVHgfthUjRuf/EGuuyi5/cLJAOC249DYbcGD18xy\ne50FkwfJt5XFYXtLOdv5h+dXBzz7+fVPB/C3/6yFxWpTraAMKUjHRMXOX86MUaT1i2DM17T1HEU1\n8MFeivQlJyZAl6BFUmKCamZMYgzSNzuiWGe12fCfr3ZijSOXqLXDhKy0xJCWBUjQatFttqLLZEZL\nu9GtmKjZYpVbn0mY+9lzdU2dePWrnWg3dENU5FhdecoYjBmWg+FFGW6zYCazBQU5qfj9WePlY/++\n41hccqKABVPsAVkwZsZcA7plGwJrt/T+8r3ybdcdk8ri3ylJnBmjyOoXP4Fmi/dvScr+YRku335G\nFGdiX3UrZo8vBGCfqlbOjEl2H4quth5EkfL8J1uxVqzHik3VmDWuEAaTBZlp/ktU9EVCggYVNW34\n/WMr5GPP3TJf7mvpmjMKAKu31mBsSW5Ix9Xf3PHCGrdj40fkYm65/Qutsql7dnoi0lL0OGuuPf9q\n2ugCvHj7MaqcQCnY6TL2PRgzuLxGUwBLla5frF0LeicqNnppWWOMIqyfBGPeZ8ZSFbkAhxs7VY/d\nuXAq2ru6kemod9TZZUaXyeJokeT85dyy7whaO03yeUTxyNhtwVrRmY9ltdlgNFn6tGEmEDqtBq5/\neps7jBiYaN8x2eio/q/RAFKljeL8tJCOqb9pafcc3Nxwdrl8Wzl7VDY4WzUbBnjfSNWXZUqr1Yan\nP9oityxyjiXByzOcvlhV4fNxFnmlaNLvlymVO7zmlRepPjC0Wo0qwJKm0//yyk9Ys61W9Trtnb6T\nVIn6u989+r18Oy1ZJ9f5y/OSixksnjboKP+Q3vPvnwGom44HYzYmnuz30gZOWSYoSzEDagsgZ0ua\neepLj8r6ZoNbIGZ/bf/B2M871Z/hnpL0z5k/Apf4aaFHFA79JBgLLJlzUH66/IF92UmC1/Nqmwx4\n6YvtqmOBFJ0k6q/aXDax5GUmY8WmagAIefuwVg9fhKRelTabTS6/MHlUPv5y+TQArKjeEzabDU99\nsBkAcPrsErcZL4lyOfpMD+UhXPWmLIkrb5unzFb/AZ7UhD473T7uv145w+2cU48qwYIpg3s9PqJg\n6RfBWE56YN/ME3Va/N/5E/Hro0dgXnmx2+PKnZeuTB5qjbUbutmmheJCY6t6Gatb8XPvmjwfDmaL\nFZ1dZix6aJl87IJjR8p5TYt/OQhLAH+wCdiyz9lWzmy1YtroApQNysKIYnWQrVymTAlgaVpK9ejL\nZ2SzS0cUqTireKAZW/cd8bmrsr3ThEED0vDodXPw0h+OQW6m7yr8RJHUL4Kxs/x8S7v3iuk4f0EZ\nhhSkY2BuKk6fXeKx+GSi3vvU94GaNtz/xlo0tNhbKXWbrbjxyR+ithcbUTBJMxRnHz0CORlJqqWn\nC48bGfbxdFusePjtDapjWq1G1e/y2Y+3hntYMae106QqC2JwzDLeeclU/PnSaapzlcvFgew+lGfG\nehmMtXSY8Nwn6n/DWY7NVpv3HsFj723Cm4tFj8/dW92Cji4zaho7odFoAipITBRJMf0TevXpY/Hs\nLUf7/WAYOjADJ80c6jdhs95Hz8o3Fu/C3qpWfPT9PgDOrdUH67iFnvq3Ndtq8Ph79j/YmWmJ0CVo\n0NBiT5ofMywHRXnhT5bv7raistY9zyldsWN6w24Wa/bnzcW7VPc7jd6T7RMU+bapARRJTZBnxnq3\nTPnVmkq3Y67liZZvrHY7Z8+hFtz/+joATC+h2BHTwVh6ij6oO7m87ShSkhJa3/nO2d/SxPwU6qfE\nA0148XNn/mR2eqJqVizJx2xyKEizM5v3hX9ptD9S1toC3MtB9IVO27eZMU9LkHkBLDVW1LT26v2I\nIimmgzFND/vc+TN2uHtdolnjBqrupybr3IIvKZGZqL956C31UuDIwdloUyTU52SEdiel0oPXzMLV\nZ4wDYK+sPlLR3Pm6X09wOz8jlVXVfek2W/Hj5sOqY8rK+a56WqJCJ7ey6t3slBTEKctYKHd3esPJ\nMIpFsR2MBfn15k8sxt9cdty4Vt/XaDRYK9apjr21ZDeI+psNLj0eH7r2KKQk6VRLP/nZKWEbj2th\nTuU4lGULjp5o35zT1tktFwc90tKFN74RYfCxDBdvrnlkuXy7vDQPz95yNCaPyvd6fnd3z2a4dLq+\nJfCbHDOw917h/EwOZHnUZmM0RrEnpoMxa5B/6TQaDQYXqHMSTptd4nZeVpr7bAA/AKg/2X+4Ff/6\naIvqmBR4KWv1ZaaFcfZJo04i31ftXI5Sbr5RNoD++Ad7juftz63Csg1V+ObnA2EYaOy58dxyvykf\nUjmJQGul9nWZUgrGEnVa3HvFdPzf+RM9Vsr/9Mf98u11Yh3eXbpHvu+pRh1RNIrpYKy3iaE9MTAn\nVXXfZrOhpcM9t4yJotSfVDd0qO4rl+uzFAFYgcvvRyjZbN538Um1pFy1tJvwz7fWy/c7u8xYueUw\nvzwpLDp1TEDtgMxm+/8zvYf2U57Iy5S9+Gxs7TBh7U77CoRel4ChAzMwYUQeAOD+q2aqzlUGY8+4\n7KD1VFuMKBrFdDskcx8qOwdK2RYJAFZuqfH44WJvoRTTsS0RAGDz3gbVLuHnb52vmnm66dyJ+Iuj\n6n1KYvgS+K1WG0YPzXY7ftclU91qSM0cOxA/ba/FoAFp+FoxG7Zk3SEA9nyy8tIBoR1wFKtSBNtz\nJhQF9JwhjlWDKT6WMpWk3ZS9qcC/QZEKkqhXf64W5aVhYmkeNgVQ3y4xgBwzomgQ0z+pocpXyVQk\n/rrWHms3dMt5J3df5qzD872HLdZEseY/X+3EE+9vxuJfDgIAZo8vdPsdcF3KDxerzeZWnub2Cyah\ndFCW27mTyuyBlg2eZ2Xqm7uCP8AYUunYcdiTJu8zxw3ErRdMwmWKZWBf+pLAr0zU97TUeMO55Rg1\nxBmYe2scnsAvyBQjYvYn9W9XzsCwwoyQvPafL5uGc+aPwMt/WAAAql96pcH56fJOH09Ll0SxRrkz\nOD1FjytPHePxvLPmDUdORlJYlimlXZNSruZ4x67nWeMGYkyJ+w5owFly45ufD3p8PN5ziaQSFguP\nD7wvo1ajwbiS3IDLmcgV+HvRCeEfr/0i3/ZUH1Kr0eDcY0rl+7c+s1JuGO9pDETRLmaDsVB+Ox+Q\nlYJTj3JW6ff27VGXoMHVp9u32iuLTRLFIilHR5KRqveaS3TGnOF49Lo5AZUa6Ks/XjQFT900T95J\nd/LMoQCANdtqvT7H2xcoibJSf38nHmhCg0tBa6l3Z1IIl5n9VeCvazZ4DKCU/nntUV4fK3OZEb3t\n2VVu5wTSKYAoGvAnNQC/WVCGxtYu1e4twP6NTVrCOVTfgbZOU1x9yFP/8t9v1dXYDx/pjNBI1LRa\njerLTmIAAYS/Egj9oW+l2WLFA2+sw4wxA3GSI0B1tWZbjVy09993HAsAMBjNqGuyB2ehLNrrb5ny\njudXq8allJuZDJ1WgwG9TEW585KpSE3SMY+XYgZ/UgOQl5WMuy6Z6vExaWbgp+21uPPFNfJxs8WK\nXQebUddswI1P/oC2TpPH5xNFg417GtDSof4ZHeehCHI06E0AccacEtV912uNNTabDVc/vBwVNW14\nb9keeXdoQ4sBNzyxQp7lVHZPAIAn3t+E6x5fgR8cxV5DWRg3oQ+Nwg3GbiQn9T5QLBuUheIB4W/T\nRdRbDMYCpNFokJdpz1lJ1Gvx3C3zAai3eXcoWon8tL0WD/53Pe54fjXaDd246akfUdsUHTMNRK6e\n+mCz2zFv5SIirTc75GaOVXfSeDuGCzVbrTYsemiZ6tiih5ahrdOEZeur0NFlxrOfbHUr39HR1Y3N\nLjsQQ9lX1FlnrGcJ/FabDQajBSkBtLo7YfqQXo2NKNowGOuBI632JP1z5pfKuRaeEkRtNhs+X1nh\ndvyeV34O6fiIesN11vaW30zEwNxUnDl3eIRG5FugS0/3XjFdvq3XaXHyLPVS3o7KpqCOK1wO1Lk3\nSAeAvdWtaDc4W1W5BmxvfasOQIvyQrv5QhfgzJhr0CjtVg8k3+vcY0rxq6mDezlCoujBYKwHrj1z\nHHIzk1TfsnUevqV/8/NB1LkkzALOitJEoVJZ09bjZs83PfWjfPuha4/C+OF5+MfVszAgK3ytjnoi\n0KRsZRPsRF0CzjumDCfNcAZkD7+9wW8CeTTaf9hzMHagpg2tPpZfV2+rUd1X9hgNBV8J/MoAzKRo\ns2QwmnHDEz8AsC+dB/IehbnhKzxMFCpM4O+BGWMGYsYY9XKHazVqm82GLfu8FyNcs70G+dkpKC12\nr41E1Fumbgue+nAztlc0obw0DzefN7HHr5GapAtrr8neSknS4Y6LpyDPpdCrq6x0Z9syqXCo1C9R\nsre61a1gbLR74xvR4/FPftzfo3I/oc6p0mo10Go0MHsokq0snP3jlsMYW5KDqnp114f87MD+XcKx\no5co1PoUjAmCIAC4EIABwHwA9wLYA+BBAPsAjARwpyiKtY7zbweQCSAHwGJRFD9zHJ8E4DoA+wEU\nALhNFMWY6OjrWgOn22xFlo9Cii9+pt7ZRBQM1z+xQs7Ncc0L8qWm0ZnHePUZ44I+rlDxV7oCUCf6\nS3+wT5g+FF+sqpSPW6O0jZnNZvNbuf7F24/B1Q8vVx2rrPE8a6b0r5vnYdXWGswYXdCXIQZEl6CB\nxcPMmHK27J3vdsvB2SJFXbtAv1Aog7Hpowtw1rzoXF4n8qXXXykEQUgA8BiAv4mi+BCARbAHUw8A\nWCKK4oMAPgHwiOP8mQAWiKJ4N4CbATwqCEKWIAgaAG8CuFsUxQcAWABc1odrCqvMND0G5ztrnhmM\nZuRlxdY3bYpdVpsNd764RpUkHWgjZwDYW9UCAJg6Kh/lpXnBHl7EXXz8KMwtL0KCI5k8PUWPuYr2\nP9Yo7VH5+PubcPYfP8eH3+9VHZdywrLSEqFL0GJQALNbN5w9Qb49tiQHacl6HD9tiGrmMFS0Wg32\nH25DR5d6SXSP4+cOUM+StSryFxN1ge2mVK5O/O6s8SHdlEAUKn2Z350OQAPgBkEQ/gTgdAANAE4F\nsNpxzkrHfQA4TTrumPXaAfts2ggAKaIo1nh4TtRL0Grxt0UzcPTEYgBAp9GML1fbv3mfMacEt184\nGRccWxbJIVI/9s6S3arZLcDeUDtQr3y5AwAwtzyw/oSx5ldTB+PKU9RdBJQzZskhrLPVW9UNHdi6\nrxEA8OXqStUs0ttL7LXgpNIcZwSwyUJZtDqUdcU86TLZi8t+9P0++VhrpwmPvbvJ4/nKmb1AC9IO\nCHA5kyia9WWZchiAowBcKIpiiyAIbwIwwb7MKP1GtQLIEQRB5zi+Q/H8VsexesX5yuM+5eSkQhfg\nN6dwyHXk2vwsOpNOj5o4COMdzYgtGg3e/865myk7J61PuQ75+aFpBRXt4vW6Afdrb2rrkhtf+zvX\nk9ueXCHfnj6hOCwzJb0R7H/zbMXMdVJKYtT9TH30437V/aUbD+Pik+z9IFc7ug6UFGUiPz8DA1zy\nrDyZNLZQvp2YqIvI9e461CK/71vvbPB63s877PXRzjh6BIYPDazOXWa2M4E/2v4te6M/XENvxfO1\n9yUYawWwUxRFab75RwDHAKgDkAGgGfb8sCZRFM2CIEjHJZmOc70d96kpymp2mR3tRT5d4VxWMBpM\nqK+3x5ltLo1s73zmB/zhoim9eq/8/Az5deNJvF43oL72dkM3nvtkq9cq8xoNUFvX6rWVkc1mwwuf\nbYN4wF7aISNVD5PBhHpD9BVCDcW/ebfJmY7a0NgRVT9TFqsVX7gEY+t31OCEqYPQqVjqW3TKaNTX\nt8Hk59/s6tPHoq3FubP7p201EbneLmO3/L67D/gvKTJVGNijcd5wzgRkpiVG1b9lb/Azrn9fu69g\nsy/LlD8ByHPkjgH2mbJdAL6EfcYMAOY47kN5XBAEPYAxAFbAnuhvEASh0MNzYsaPm6tV99OSdRii\n6J/Z5vKhufNAM5asPehWY4fIn8ff24QdlU1YJ9arjms0wMTSPNhsQJfR+/6Xpeur5BkIABACSIbv\nT5R1ykyOL1GR0NxuxOJfDqrGsHR9ldt5GY5lxg27nbPuUl5qsp/CqLPG2T9Wpc+iRV4av4ee84vB\ntNH5fs/2187K1eSR+dyhTjGt1zNjoig2CoLwRwBPCIJQDyAfwN8ApAB4SBCEUQBKAdzmOH+NIAjL\nBEF4APbdlLeKotgMAIIgLARwvyAIlQASALzWl4uKhOZ2dbA1eWS+aqfl2UeXYuUWdZ2ft5bsRkqS\nDnMm9M98HQqN/YfVPVJvv2AScjOTkZuZLJc9aGjpwtBk91Y363fVu/WgvOKUSP2BjozxI3Lx0Qp7\nDtM6sR7HTYtMFfdbnl4JwL6b8Llb5qPNYMLHK5y5VSfOGoZv1lSi2JGQvn6XPfg+++gRchCW4KHo\n9C7i1c0AACAASURBVAnTh2DxLwdVx+5cOBWdRjNyMiK/FB3IBtZkNvimONOnn3hRFD8G8LHLYQOA\nq7yc/7CX4xth343Zb0h1jSQ5GUm4b9EM3O1Shb+hJfaKTlLkuM7knDJrGMaUOHNrMtLsAdhLX2zH\nX6+YAa1W/cf66Y+2qO5fe+a4gIuo9hclhZn49bzh+PiH/RAPNkd6OACA3z32ver+mGE5OH7GUHyz\nxpnAL82MDS/OlM9zDcWuOGU0Rg3OxuJfDmLWOGdNxKTEhIAT4kPhSGsXlq0/hAVTBvuctZXY82m5\nakDxg9XyguS8BaWq+3urW93OGZSfjpf/sEB17FOX/BAibyxWK+599RfVMdflHKmEQ1V9B7ZXNsJm\ns2FHZRPMFitM3RakuZw/emhOaAcdpSI1GwbYZza/+qnS5zkXHT8KiY6dj6Zuq6rmmHJZ2eIyzWSx\n2jAwNxX//N1RuPREIYij7rs3FttnZA0m5xeKm88r93hupo9ajUT9UXx9JQ6hEUWZqvsWL81xXWcq\niAL17tI9bmUsXGdWExQ/Xz9tq8Wug82qIqeSh383GxpN/P7RC7S/ZbBZbTbc99pav+cV5abC4hjj\nd+sPYflGey6ZBr7HLm3aiNZWVoCz9+T5C8owZpj7l4FTZg1DRmoiujqMbo8R9VecGQsS1w+/E2d4\n/+Z916VT5du5mZHP4aDYsGStexkL15mu6gZnqYOVW2s8BmKAPQE81toABZOnXKtwMASwRAfYv7Sl\nKXL+pBkw1694QwrScZyiUbZre7ZoY7PZcPiI/Wd0/qRi6D2UJyrIid5AkihUODMWJK6JsSMHe9/Z\nM0DxR9BfyxMiV4k6Le65Yjr+t7oSJ80c6v8J5MZb2Y9Q21npv6yDJJBZS41Gg4uOH4XJIwdgybpD\nAe1UjKR//Hc9DtS2A3DvKZmWrENHlxlThei+BqJQYDAWJK7Lj74+7BMU314ZjFGgUpN06DSa8dyt\n86HRaLDotLFu55wxpwS/7HSWrSjKS8XhI+qlzYuPHxXyscaCYYUZ8ixNOHR2mbHFUVnflwevtVcG\ncu1768uYklzVRo5oUVqcqcqf3XPI2QYpweUz8+LjR8mlOIjiDYOxEPG1NTs1WYfRQ7Ox80AzukwW\nmC3WiOWwUPT7YlWFXIphWGGGzz/S6SnqchaugdhJM4biV4plrXimT9B6ze0MNpvNhuufWOHznFvO\nn4jRw3L61WfBHQun4Kp/Lvf4mOvPcSR3exJFWv/5rY8ip80ucfujqKTVaFTV9z9YvtfruUQfKWpP\nJfppoZWZlojjfewUPHv+iKCNK9bpEjSwWG1haRYu9ZL0pSA31S0Qu+KU0ar7J8+KrWVpaXdvIKI9\n340olPjTHwIn9zCPR7ms1Fvfrj2IZz/ewor+/Uyty+5Jf8GYRqPBhceN9Pp4f5p16SspXSDUs2P7\nqltx10s/eXwsT5E/mpPuniM2r7xYvn35yaNxzvxSt3P6i0CKwRL1V/xkDoGe/sFrajOiQdE/rjfe\nXrIba8V6HKxr79PrUHT504trVPeb2qOvf2Ss0jlylqSiqqHy99fXuu2ivPU3k/DrecNxjmKm0tPO\nQqWjJxZHbONBX/zxoskBneea0E8UT/jTHwKBbpu/+nRnAnZfliqrFOUMXIuCUuzy1DdRWboiUL89\nzd7uaFih9ya18Uj60uRaODUcxg3Pxelzhgf0b/LHiybjrkum+j0vWglDc3ymbdx92TScPHMohKHx\n1SOVSIkJ/EF0y28mouZIZ8DfXpUfxK79Br3ZdbAZGr36n+3Zj9Utbq58cCluPKcck0YOCOg1KfpY\nrFZ8trICgP0Pt16fgI276n0/SeG8Y0rxviPAnz2+CDkZyRiUnxaKocYs6UtTKGfGtu33vXuyKM//\nv4nQD7ok+GrIPrwoE8NdimYTxRvOjAXR+OF5PWqzokxYtfr4e9BttuJQfTvaDd148L/rccV9i1W5\nYa475gDgqQ83BzwOij73vvoL/rfGXrB17oQiXH3WBORkJOHqM9zLWXgycoh6lmHMsBxkpsZntX1v\npJkxs8WKdWIdmttDUPHdw/cy10K9t/5mEu65fHrw3zuKJDBXkcgnzoxFkPIDyteOruc/3YoNuxtw\nlWJZs6Kmjd8m+7Gqeudy5LjhuRgyMAOPXjcn4OcPKUhHSWEGjpk8KBTD6xd0jpmxPYda8OLn25GT\nkdSj/8eB+OSHfar7Gal63HL+JNWxccOjrz5YsOki1PGAKFbw60oEKRNWm9qMMHqYyjcYzdiwuwEA\nIB5olo93OZrtKqf/F/APb7/Q2dUt377/qpk+8228SdIn4C+XT8fRE4v9nxynpLILP22vBWD/HQy2\nvVXq9IPjpw2Jy9w97uIl8o2/IRGUnqLHrLED5fs/bj6setxqteG6x52FItcrcoYefnsD1myvQUeX\nfZfWwNxU/ObYMtXzQ71LjELj7SW75duB5BRR70g5Y5v2Hgnaaza3G2H1sSFgwZT4/MI0sUydv3rZ\nSUKERkIUnRiMRdjVZ4yTb7u2RupQzJAAQLtBff/Fz7bLx8aV5CBRr94aH5IcGAq6l7/Yjhuf/EHO\nA1y1rQYAcP6CMl9Poz4K9mxNbVMnbnl6Je58aY1bvb/7r5qJ52+dr2r+HU/OO8ZZH22qkI/5k+Iz\nKCXyhsFYFOkyqWsRuQZfnjS1dQGA/CH/7zuOlfOE9lS1YF91YLs0KXJWba1Bu6EbnUYzftx8GNLf\ncTYBDy3X3oh9td/xu1bXZMB36w4BABL1WgwbmIGivDS3L0vxJEXRHu66X0+I4EiIohODsSgw2VGC\nYthAdS6Jp2DMtbp6dYN9J2WqYoeWVKX9xc+24++vr2VV/ijWqmiTU3G4DTsPNEVwNKTU0m4MuJG4\n0WTBf7/dJd9fJ9bDarXB1G1FMnsuEpEf3E0ZBUYPy8GG3Q1uxSeXbahyO9c1r6yu2V65X/mB3+lS\n7bu6oQOD8tODNVzqA4PRjI27GzBz3EC8t3QPFv9yUH7s0Xc3yrf7e6mDaNXSYUJWmr0EyP89vRIA\n8MofF/hszg4Ai9celPM3AfsXKenLVGoyP2YB4Ikb5wL8XkjkEWfGooBc78il2NiabbVu57omBy93\nBGzJic4P/Ckj81XnPPbepqCMk/ru9W9EvPTFdjz5/mZVIOZqcAET90PNU3xldKQKKPM3XXM5PWl1\naQRemJuKA3VtAMAvQg6ZqYnITGOtOyJPGIxFAalHXiANiwflp+H+381W9bQD1N++XSvvN7UZuVQZ\nBTq7uuUyClv2ed/Bt/CEUXLZBQov6bdEWRfLU8kZpeZ2o5wjJmntNGHFxmoAQFFualDHSET9Dz/x\no4C0xV65TOlte/ylJwooL8tHsUvJg4xU37u0XJcuKfw++XG/18cERcX8AVkp4RgOeSD93mk0Ghw1\nrhCAPR/Ml1scy5lKuw+1YK1oL0XDnDEi8ofJDFFA2ZZFsmlvg3z7TwunYHB+Omw25wxYTaO6BVJG\ninr6Pz1Fr9oAYOgyx+22+mhgtljdZk+UxIPOgr65mUnhGFLc8zRZrJydljZb+psZU7ri5NF49aud\nqmPxvIuSiALDYCwKSEtSZscfgm37G/GvD53NvzNSE1VbwwG49bxznRl76qZ56Owy4/on7EVjV2+r\nwelzhgd55BSoqvoOj3/8T59dgsy0RBTlpeKRd+wJ/HmZyWEeXXzy1ILMZLbiL6/8jKz0RLnJt7Hb\nd85YVnoiWtrtOWMDPSxJJjEYIyI/uEwZBZzLlPYP/Z93qBP3Cz18wB8zaRCK8pzHPX37VuaR/bKz\nLihjpd6RCvCePGsoHvn9bPn4mfOG41dTB2NsSS5+f9Z4nDN/hHvgTSFh8xBjHWntwqH6djkQA3zX\n+7PZbGhtdybvZ3lIUE/U82OWiHzjp0QU0DuWKU3dVhw+0oEfXMpXeJKSpMN9v53p9zypivvIwdl+\nzqRQ2lvdAgAozktDbmYy/nntUXjulvnQKrb0TRtdgFOPKonQCOOPp5kx1+V/AD5rjZktNlW1hqz0\nRAzIUs9sMj2AiPxhMBYFBmTbP7xrGzvx7tI9AT9Pq9HguVvn47lb5ns9RyooW90QWPFKCo0vVlUC\nAMaW5AIABmSnIImJ3RHlaZPMxyv2uR1r6+zGzztqscbRpkpisVpxzSPL5fu/njccyYk6tz6MaSmc\n6SQi3/gpEQXyHbvnmtuNqnphAHDBsb77E/rLR0l2LHkpE8QpfPZUteCFT7fJ93MymJwfLQKt9tLS\nbsTza+zB9CzHDksAqKxpV50n5WSeM38EukxmrNxiD96YM0ZE/nBmLApIK1VWG6DTqf9JNu31Xo8q\nEGmKvDFPSzAUOt+uPYgH3liHI61dkR4KeeBpmVJp/HD7LGZjm9Hj4zYv5eSTE3U4ftoQ+b6/6v1E\nRAzGooBGo4FGY08GXuuSaD9/UnGfXluXoJW/mQfaZ4/6zmqz4e0lu1XHhhdlRmg05Ilr+zGlE2cM\nwaUnCQCAji7PCfwVh9vk27+ep96pnJXOGVAiChyDsSih1Wg8LptMdmlt1BunzR4GAEjQatDWafJz\nNgXDNz8dcDs2ehg3UUSTueVFXh9rN3TL9f8O1DqXIzsVgVmhYjfztNEFqudnpSXipnPL8bcrZwRr\nuETUjzFnLEpoNOpv6ok6LZ69ZT602r4vceh19pmxJ97fDAC4+bxylJcO8PUU6qP3l++Vb5+3oBSJ\nugQcPdH7H38Kv7JBWbjrkqm4/411bo+lJOrkYEypy2RBqmN35JerKuTjRXnuvURdE/mJiLxhMBYl\ntBoNus3OSt9P3jQvKIEY8P/t3XmcVNWd9/FPLzTdDc3egIAwEeEnKiquIG6IiRqXGE3yaELEiZIx\nURMd1+ijcYz6ch19omZ9TDTxGRNHHcc8LjFG0ARRg0tk/YmCGPYWGmi2bnqZP+6t6uru6rbpqq7q\nqvt9/2PVqXOrz89bnPrVueee0/ausefmrVQyloKGxkY219Tx1Gsf0a+8hHOnj2ND9Q627tjNviP7\nt6h726yjkn5RS8/Qqzj5xYFexYUUJfn3l7hp+LadwRZjN5x/WPc0TkQiQ8lYD1FX38iqqmBO16Rx\nQ9J6B9buhparW+7UPpVd1tTUxKy75rQqCybrA9zxL5P5dEvzhH0lYj1bstEvgKKiwqSvfbBqM8MG\nlbNt525WVQWXL8eO6N+mnojInlAy1gO192u9qxpaJWP1DZ28p1/i6sL9CRevrG7zWiwRA9iyvS6+\n28FBYwdnpnHSZcVFyUefpx44PL4zRqLqrcGdla++t7pb2yUi0aJkrAfauj29k+xb3zXW1NkFlgQI\nLvNefO+rAOw7quNRkKdeXc4H4Zpu504f1+1tk9QUJll24saZhyfdYxJgRziqXFHedtsjEZGu0t2U\nPdDST9K7QOv0w0a1eP5Z6ytJs7rdDVx01+z48w9XBdsaHTx2MFMSFgA965hgaYMPEhbX7VeubXB6\nun59SijpVcixCXdWJo5M9y1reQ5jI6T/9Zdgpf7YncoiIqnQyFgPlO4Vuwf07U3lgFKqNgdzmerq\nk+yQLG388g+LmddqC5yY73/1YAAuOn0CAG97VZs6pdrwu8cr6VUU304stidsYjLWepPwN5es59zp\n49gSbg4+emhFhloqIvlMI2M90GXnTEz7e8YSMQg2JM9VtbsbWnxBdscl1y3barniwb+2m4glChbs\nLaCi1SjYg5cfm/QSmPQ8sXMYU1zY3C3G9naN7WSxs7aB6oQV+Ut6qQsVkdTpp3sPNKCbV+/O1bsp\nN9fU8p1w7taY4RWs2rCNhsYmphwwnFln7A/Am4vXs/rT7Zx93D5d/jv3/P69+MhHzC+uPoHqmlrm\nL93A0RPbrheWOJfshvMPi69FJbkncUmZGV8wNtXUcv7Jxo8enc+IIX1YX928rVhsDT8RkVQoGeuB\nuuPXduJlSoAVa7fm3PY8v3l+cfzxynXNW9HMW7SOWWfsT3VNLT9/NtiU+7TJY+hd0vxFWbOjjr5l\nvTq1T+DqqpbbRj10xXEUFxVSOaCMUycnnyNUVFjIr647cY/ikZ5l7Ih+fLRma4v9XAdW9OaHFxwB\nQO+SIoqLCtickKiXpPnOZxGJppSTMTMrA94EXnL3q8xsEHAHsBwYB1zv7uvDulcD/YCBYf1nw/JD\ngEuAFcBQ4Cp3z83hmy761hcn8KvnlwBQ0g2/tm+ceQT3PP4un2wI1kZ6/M/LuH5G7ixWubu+kT+9\n1XaLoZjla7Zy62/mx59v37U7noy9+0EVDzy9gG+fsT+TEybdJ3rt72uo3d0Q3xwaYOYpxtSJe7W7\nFpXklx/MOIxddQ2UtDNns6iggMbGJt5IuHyd7mVoRCSa0tGT3Aq8m/D8duBld78DeAa4B8DMjgKm\nufuNwOXAvWbW38wKgMeAG939dqABmJmGduWU4Qm30ndHB9+3rBc3J+yTl2u/6BMTrdYKkrx+22/f\npraugW/d8QoPPL0AgCdmf9jm2MamJhYs38gjLyzl8ZeX8Ydwi5vph47i+ENGKhGLkMLCAspL2/99\nWlRUQENjU4u7nXVjsoikQ0ojY2b2TWAucBDQNyw+DbgtfDwXeDR8fDowD8Dd681sCXA8sAgoc/d1\nCcfMAB7u6G8PHFhOcR7N19iyq3krpFEjBnzmVkiVlandxVVSUpzye2TSpoRJ0zNO3Y93vYpFyzcG\nBQVAqy/F6ppa1m2tbVG2bWd9m5jve/wdXklYtPWNResBuODMAxlQ0b1z9/ZULp2vdOopcVeUl1Bd\ns6tF2Yjh/ais7NvOEanrKbFnQ1Rjj2rcEO3Yu5yMmdn+wAR3v97MDkp4aSgQm9CzFRhoZsVh+ZKE\nelvDsqqE+onlHapOmESbD2q27ow/3rhxW4d1KysrqKqq6bDOZ6mtrWfDhq1UbdlFZf/STs2lypam\npia279zNqKF9uei0CYweVsGJB49g/tINPDdvJSvXB/8vSkuKuPmfj+C6n79BWe8i7vpty9Gy+oZG\nln5YxeD+pfGyxEQs0e5ddVTtSu/iu6lIxznPRT0p7jWftpxLeNHpE+hFU7e1ryfFnmlRjT2qcUM0\nYu8o2UzlGsyXgV1mdh1wDHCkmV0ObABif7EfUB3O/0osj722oYPySCnO8GXDJSureeHNT7juZ/P4\n0/xVGf3bndXU1MRrf1/DhXcGi65e+tVDGD2s+aNy+H5D6deneSX00pIihg4sp3+fEnbWNiS9a/Tq\nn77Ot+54hZoddazduL3N6yKdMf2wURx9YNu7akVEuqLLGYC73+but4Rzw/4KvOXu9wPPAVPCalPD\n5ySWm1kvYALwGsFE/51mNjzJMZFR/BmXJdPlki8fGH/85JyPAPjdn5dl5G/vqUUrNvHIC0vjz0dU\ntt10e0HsUiXE73Lb0mo7qQcvP47/871jWpQ99PQCbvjlmy3KRoXvX5ShcyG5qzJhdFVEJFXpuJvy\nHOA4oMTMzgOuB+40s/HAWOAqAHd/w8xmm9ntBHdTXunum8P3mAHcZmYrgSKa55lFR4a+/4f0L8vM\nH0pBY2MTf3l/Df85+6N4me09gIEVpVTtarki+uhhfflkfXBZ97iDR7R5r6J2JmWv2dh8mfviLx3A\nqMq+DO5XysPPL+ELR+ydrlAkj0ybNJLZ7wYbhOsuShFJp5STMXd/CniqVfGsdure3U75e8CFqbYl\nl8W2QOrunKy0d8+/6eHJOR/xYqtlLK79xqFJ6846fX9ufPgtAI49uO1lo59eeXz88amTR/PCG8H7\nJq7if+SEYfHH3z2reeRQJNHxh4yIJ2OZnlYgIvlNPUoPUVFewtXnTeLu7x7drX+ntKTnr/PbOhG7\n/7Jj2qkJIxPuZItt6nxdmLiNHdGvxdIUZx79uTbH3zjz8JTaKtHRP2FnDI2MiUg6qUfpQSaMGcig\nft07F6WsJPnI2KebdyYt724frtrC6k87nkifOEk/mRlfGM+EMQMZHP6/G7/3AB64/Fiu+fqkFvV6\nlxRxT6tkN9d2IZDsqShr3uKqqFBdp4ikT88fJpG0au8X/dYduxkyILPzyRqbmrj9sbcB+OU1J1BU\nWMj2VnPCRnViDacTDx3FiYeOalHWp529IROT3eOSXNYUaU/i2n9jhkd3PSQRST/9vIuY9tYT++v7\nazLcEqhJuOtx1l1zaGpqYvY7wZycfUb0o09pMV87cWza/+7N/3wEk8YN4Ssn7Jv295b89uPvH8ut\nFx3F0Az/cBGR/KaRMQFgzntrOGXymIx9yeyqq+eKB+e2KHtu3kqefm05AJPGDeGLk8d0y2K0o4dV\ncNk5B312RZFW+pb1is9NFBFJF42MRdzUic0bZ2/fubuDmum1cPmmNmWxRAygX3lJj94VQEREJF00\nMhZxiRORCzOU/Fx632vsSLI6fqKBPWxfSBERke6ikbEIevjaafHHZQnrjjU2NSWrnlb1DY1tErHE\n0bmYYYPKu70tIiIiPYGSsQhKvPy3aEXz5cLd9Y1t6lbX1PLOB1Vp+burNmzj23fPaVF23TcOZf9/\nGtSi7LKzJ1KpCdIiIhIRSsYibtqkkfHHdfUN8cfPzfuYOe+t5sqH5vLg0wtYt2lHkqP3zE2/eqtN\n2fi9B1Daq+XaZ5PGV6b8t0RERHKFkrGImzqxea2t9ZuChV8bGht56tXl/OZFj7/28dqtXf4bH6/b\nyotvftKmfOyIYMHV7buaL1seM1Frf4mISLRoAn9E/eiio9hVV09JryJuufBIbnr4LVZVbWPtxu3c\n8Ms329Sf894aJh/Qdm5XZ9zyyPw2ZTNPsfgI2AGfa75Mue+o/l36GyIiIrlKyVhEjRzSJ/64vHfw\nMaita2D+0g1J6/9TF1ccb0pyU8BV5x7SYp5Y4p2TRyVs2i0iIhIFSsaE4nCLpPqGRtZXJ9+j8qW/\n/YOxI/tzxH5D9+i9l6ysbvF82qEj20zYB3joiuPYWVtP73b2zhQREclXmjMmFBfGkrEmXl+4rt16\nP31mId+64xV27Or84rBrWm0CXtk/+V2SZb2Lu32TdBERkZ5IyZjQqzhY6qK+oZFxnZiz9f/nrez0\ne//Hy8sAqCjvxdiR/bQ5t4iISCtKxiS+Cv/CFZvY1oktkZLdGZloffUO/u3Xf2NFwh2Ys87Ynxu+\neTjlpdrXT0REJJGSMaGwsHkR2LUbW64n1pWlJp6c/REr19fw4yffj5cdkGSemIiIiCgZkw6cN30c\nM081Ljt7YqePqa6p5e1wxf4t2+vi5dr0W0REJDndTSlJPXzttHgClWxifX1DI8VFbXP5nz6zsE3Z\nudPHpb+BIiIieUIjY5JU4kjWmOEVXHbORCYfMIy9BgcbeFdtTr4Exoert7Qp69+npHsaKSIikgeU\njEmnFBYU8Mai9fHNxJetapt0NTS23WgclIyJiIh0RMmYAPCDGYd2+Hr1tloADrdg0detCfPBYuYu\naF6jLDEB699XyZiIiEh7lIwJAHsNbt4eaeqBbfegPGbiXlxz3iQO2y/YT3LZqi3UN7QcCXvkhaXh\ne5Vz58VTqBxQyrhR/Rk+qLwbWy4iIpLbNIFfACgvbf4oNLbdTpLiokL2GzOQ9dXB0hcLlm/k23fP\n4cRDR/L1z49n8ceb4nWPmjCMkl5F3Hnx0d3ebhERkVynZEyAYE7YXoPLWbtxB7vq6tutV1HWctHW\nV95Zzb6j+vOLZxfHy4YM0LZGIiIinaXLlBIXu1S5utV+komSraC/akPL+nu6mbiIiEiUKRmTuMHh\nemJbkkzOTzSg1YT8uQvXxh8fNHYwvYqL0t84ERGRPKVkTOIODyfnf/7wUR3Wu/eSqS2eb9nWnLy9\n/9HG9DdMREQkj2nOmMSNGzWA+y87hr5lHW/mXVBQQFnvInbWNrR5bfTQvt3VPBERkbykkTFpoV+f\nkhYbh7fnoSuO57iD224iPm7vAd3RLBERkbylZEy6bPigPm3KanZ0PN9MREREWlIyJl02bdLINmVj\nhldkoSUiIiK5S8mYdFnvkiJmnbF//PmlZ0/k5CNHZ7FFIiIiuUcT+CUlgyp6xx8fOr4yiy0RERHJ\nTRoZk5QMSEjGREREZM8pGZOUlGiBVxERkZQoGZOUFHViGQwRERFpn+aMSUoqyntxwqSR7Dda64uJ\niIh0hZIxSUlBQQHnn2zZboaIiEjO6nIyZmZjgVuBd4BRwEZ3v8XMBgF3AMuBccD17r4+POZqoB8w\nEHjJ3Z8Nyw8BLgFWAEOBq9y9vstRiYiIiOSIVEbGBgG/c/f/BjCzxWb2HDALeNndnzCzM4B7gG+a\n2VHANHf/opkVA0vM7FVgK/AYcJK7rzOze4GZwMMptE1EREQkJ3R5Ar+7/y2WiCW813bgNGBeWDY3\nfA5weqw8HPVaAhwP7AOUufu6JMeIiIiI5LW0zBkzsy8Df3T3pWY2FKgJX9oKDAxHwoYSJGAkvDYU\nqEqon1jeoYEDyymO8LIKlZXR3HYoqnFDdGOPatyg2KMoqnFDtGNPORkzs2nANODysGgDUAFsJpgf\nVu3u9WYWK4/pF9Ztr7xD1dU7Um16zqqsrKCqquazK+aZqMYN0Y09qnGDYo9i7FGNG6IRe0fJZkrr\njJnZacDJwPeB4WY2BXgOmBJWmRo+J7HczHoBE4DXCCb67zSz4UmOEREREclrqdxNeRjwe2A+MBvo\nAzwEXA/caWbjgbHAVQDu/oaZzTaz2wnuprzS3TeH7zUDuM3MVgJFwKNdD0lEREQkd3Q5GXP3t4G+\n7bw8q51j7m6n/D3gwq62RURERCRXaTskERERkSxSMiYiIiKSRUrGRERERLKooKmpKdttEBEREYks\njYyJiIiIZJGSMREREZEsUjImIiIikkVKxkRERESySMmYiIiISBYpGRMRERHJIiVjIiIiIlmkZExE\nREQki5SM9UBmVpntNmSLmY3Mdhuywcz2M7OpZha5f5NmNjrbbcgWMxua7TZkg/q46IlyH9cZCUe+\nvgAACMFJREFUWoG/BzGzMuBs4DRgCfB7d/8gu63KHDM7H7gOuN7dnzGzQndvzHa7upOZlQNfBE4G\n/gDMdvea7LYqM8ysL3Am8BXgE+B5d38pu63KjDD2s4BjgI+Aue7+upkVuHvedsrq49THEaE+bk8o\nQ+0hzOww4EHgY+AGYCpwSDbblClmVhQ+LATmA18xs77u3mhmBVlsWiYcC3wK/AuwGKg3s2KAfI49\n/FK+BqgFLgGKgMFZbVRmfQ1oBG4GmoCrzczcvSlfz3vE+7jYd636uIj0cXtKyViWJSQi1QSd1Ovu\nvgL4CzAxW+3KhFjs7t4QFg0niLsG+LqZDc7HUYJY3GEH/SWCL+NzgfOBu4BrAfI59tA3gQ/dfS2w\nGdjHzD6XnZZlTnjezwUWuvs64HGC0bGrIT/Pe2gTsIII9XEQJBwJo1/DiEAfB0HcYbIVqT6uq5SM\nZYmZjTCzHwBXmdlUd18O3J/w4VwGzAnr5tX8itaxh2WFwBrgUWA5cDHwr+FrefHrqVXcx4Ud9N+B\nu4H57n4T8Dww3cxOyGJT065V7Me7+07gMeA2M3sMKCEYHXvEzE7JZlvTzcw+Z2bfNrN+AOF5fxu4\nKayyBngG6GtmlqVmpl1C3P3DorXAgxHp4+LnPBztLDKzXsBq8ruPaxF3eK4XAneS531cqpSMZYGZ\nTSC4NPMcsBK418w+3+o6+gRgblj3vCw0s1skif3fzeyk8AvqcOAbQCWwCCgys/H58OspSdz3mNlJ\nwCvAWOCIsOpfgLeA3dloZ3doJ/Zp7n4j8ANghbtfC/wI+DNQkbXGppmZlRBcjj2bYIQg5jFgtJmd\nEn6+VxOMHG3OfCvTL1nc7r7L3RPjy9c+LlnsDe6+Gzga+Dr52ce191n/I8G5Pjx8nnd9XDooGcuO\nvsAEd3/f3X8HvAicZWYHAphZBdCf4AP9c6A2X3450Tb2F4CzzexYgknc6wjmkywGvgocmyexJ4v7\nLKCUYN5QbJTkQGA0wWhJvmgd+3PA18xsHDAemBnWm0IQ/9LsNLNblADvAy8DU8xsn7B8GfAIcJ+Z\n9Sa4RF9McDknHyTGPTl2+Tk2dyq8gSFf+7jW5zwW+2CCpDtf+7j2PusfA7eQ331cyoqz3YAoMLP9\nCH4tvEwwZFsNbDazKe4+j2DY+m6CDnkhcBJwYXj4d9x9UeZbnR6djP1Ogs/iT9x9R3hZ4xPgZHf/\nMEtNT0kn4n6EYO7EMHd/wMzGmNmtwA7gandfnaWmp2wPPu9jCH6InGtmjxJcsr0ij2Jf7O7bzOwX\nwMGAESQf97l7HfATC5a2+EF4+A/dfUM22p2qTsR9FkHcsblT08nPPq6j2Dea2U/cvToP+7iOPusN\nBFd/huVLH9cdtLRFN4ndom5m3wH6EUxcnRa+/F2CL+N3gV+7+xYz+zFQ5+6xeVR7h6MIOacLsT8A\n7HL3qxOPz0LTU9LFc17v7v8ajhiUuPuubLQ9VV085zvd/RoLbn0fFk7qzjntxH480MfdL0io9z2C\nUYH73H1JQnmxu9dnuNkpSyXuPO3jOor9fndf3Pr4DDc7ZSme85zu47qbLlN2g3DIuSx8OgB40d2f\nAP43wd0kRwL/QXAn0QVhvcXAawDuPjeXOyn2PPZFBPMIgNy8wyaFcz4HgkndudpJpXDO/wrg7jty\nOREjeew3AeeY2RcSqv8nUEcwZ+6ScI4NuZqIsedx3xuLO0/7uI5iv7vVOc+nPq6z5zxn+7hMUDKW\nZmY2Bfh3gg73AIJfDWMA3H0jwfygB9z9j8CvgSPM7HaCuUN/ykqj0ySqsUc1bkg59pxe4LUTsf8Q\nuCfhkCKCpQ3eA34TXqrMOSnE/S45HDfonBPBc54pukyZJuGE1JsJJuY+Afxfgg/iZuBSd98vrNcb\n+G/gKndfaGZDgCJ3X5+VhqdBVGOPatyg2Ol87P8FXOvuC8LYS919VVYanqKoxg3RjT2qcWeDRsbS\nJ3Z7+svuXg38G3Ckuz9IsOLw5WG9wQTbgCwBcPdPc/mLKRTV2KMaNyj2zsa+lOBydCz2XP5yimrc\nEN3Yoxp3xuluyvTZATzp7v9IKJsX/vdG4BQzuxvYSrD4XUPrN8hhUY09qnGDYu9s7G/nUexRjRui\nG3tU4844JWNpEk7ITPzAjiEcDSBYf+V2goX+VoTX2PNGVGOPatyg2Ilg7FGNG6Ibe1TjzgYlY91n\nL2CTmT1OsBnyS+6+MsttypSoxh7VuEGxRzH2qMYN0Y09qnF3O03g7wZmNhx4HVgAPOHu/y/LTcqY\nqMYe1bhBsRPB2KMaN0Q39qjGnSkaGesejcDDwD3uXpvtxmRYVGOPatyg2KMYe1TjhujGHtW4M0Ij\nYyIiIiJZpKUtRERERLJIyZiIiIhIFikZExEREckiJWMiIiIiWaRkTERERCSLtLSFiOQtM5sK3Ars\nT7CR8UCgL/Brd3/yM469ADjB3S/o5maKSMRpZExE8pa7zwUeJdiu5WJ3/1/ARcCNZnZFdlsnIhLQ\nyJiIRIq7rzWza4CnzOxp4CFgETCYYFPzn5nZOGAGMNLMHgT+4O5/NLPvAeOBncAA4Ap335adSEQk\nXygZE5Eo+hvQBxgK3OvuswHM7H0ze9bdl5nZYwSXKS8NX5sOnOnuJ4XPbwWuAW7KSgQikjeUjIlI\nlBUCJ5jZecAOYBAwFliTpO6pwBAz+1n4fAiwNiOtFJG8pmRMRKLoCGA7cCIwyd3PBDCzQ4CiDo6b\n5+7fCesWAOXd3VARyX+awC8ikWJmw4G7gB8SzBPbFJYXAqMSqu4CisyswMxmAi8C08ws9iP2LODy\njDVcRPKWNgoXkbxlZlOAHwEHAk8SLG3RH/itu//ezEYDvwOWARuBLwHvAxcCZcBTwIfAK+7+KzO7\nHDga+AdQClzp7rsyG5WI5BslYyIiIiJZpMuUIiIiIlmkZExEREQki5SMiYiIiGSRkjERERGRLFIy\nJiIiIpJFSsZEREREskjJmIiIiEgW/Q90ezTcN585tAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113612b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run A_pyt/m_Excel_read.py\n",
    "plt.savefig('../images/A_pyt/DAX_history.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rapid Financial Engineering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MCS call value estimate is 3470.889\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsgAAAGoCAYAAABbtxOxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11afbce80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run A_pyt/n_pandas.py\n",
    "plt.savefig('../images/A_pyt/DAX_hist_rets.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 4650 entries, 2000-01-03 to 2017-10-31\n",
      "Data columns (total 2 columns):\n",
      "Close      4533 non-null float64\n",
      "Returns    4463 non-null float64\n",
      "dtypes: float64(2)\n",
      "memory usage: 109.0 KB\n"
     ]
    }
   ],
   "source": [
    "DAX.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Close</th>\n",
       "      <th>Returns</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2017-10-25</th>\n",
       "      <td>12953.41</td>\n",
       "      <td>-0.004604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-26</th>\n",
       "      <td>13133.28</td>\n",
       "      <td>0.013790</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-27</th>\n",
       "      <td>13217.54</td>\n",
       "      <td>0.006395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-30</th>\n",
       "      <td>13229.57</td>\n",
       "      <td>0.000910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-31</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Close   Returns\n",
       "Date                          \n",
       "2017-10-25  12953.41 -0.004604\n",
       "2017-10-26  13133.28  0.013790\n",
       "2017-10-27  13217.54  0.006395\n",
       "2017-10-30  13229.57  0.000910\n",
       "2017-10-31       NaN       NaN"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DAX.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13229.57"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2383256171114719"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 13229.57      ,  13229.57      ,  13229.57      , ...,\n",
       "         13229.57      ,  13229.57      ,  13229.57      ],\n",
       "       [ 12940.86895859,  12678.33603906,  12975.72262823, ...,\n",
       "         13512.71007441,  14040.31584158,  14369.20023542],\n",
       "       [ 13137.10612791,  12430.61667917,  13447.91404941, ...,\n",
       "         14298.23492924,  13394.77007058,  14754.44653132],\n",
       "       ..., \n",
       "       [ 11483.50634762,  13192.61799675,  11665.89998702, ...,\n",
       "         13447.76594665,  21535.57846702,  19668.47314616],\n",
       "       [ 11177.45509977,  12540.6694008 ,  12019.8728195 , ...,\n",
       "         12991.79268869,  22104.32064105,  19740.64980773],\n",
       "       [ 11361.50961507,  12096.91165357,  11992.62137337, ...,\n",
       "         12876.89257187,  22022.72946175,  19771.52245508]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:training@tpq.io\">training@tpq.io</a>\n",
    "\n",
    "**Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://python-for-finance.com\" target=\"_blank\">Python for Finance @ O'Reilly</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Listed Volatility and Variance Derivatives** |\n",
    "<a href=\"http://lvvd.tpq.io\" target=\"_blank\">Listed VV Derivatives @ Wiley Finance</a>\n",
    "\n",
    "**Python Online Training** |\n",
    "<a href=\"http://certificate.tpq.io\" target=\"_blank\">Python for Algorithmic Trading University Certificate</a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
